Network Learning 2

Setup

Read in data

True network structures

# must run analyze/convert_combine_csvs.Rmd first
data_draw <- read.csv(paste0(draw_dir, "network_learn2_draw_data.csv"))
data_ego <- read.csv(paste0(ego_dir, "network_learn2_ego_data.csv"))
ego_els <- read.csv(paste0(ego_dir,"network_learn2_ego_edgelists.csv"))
data_demo <- read.csv(paste0(ego_dir,"network_learn2_demographics.csv"))

Analyses

accuracy_draw <- ddply(data_draw, .(ID, Structure, Condition),
                       summarise, correct=mean(correct))

summ_accuracy_draw <- summarySEwithin(data = data_draw,
                                      measurevar = "correct",
                                      betweenvars = "Condition",
                                      withinvars = c("Structure"),
                                      idvar = "ID",
                                      na.rm = T)

mylm <- lmerTest::lmer(correct ~ Structure + (1|ID),
                       data=accuracy_draw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	3.426569	3.426569	1	239	376.6133	0

# which network structure did participants learn better?
# - natural
mymeans <- emmeans::emmeans(mylm, "Structure")
knitr::kable(confint(mymeans))

Structure	emmean	SE	df	lower.CL	upper.CL
natural	0.9284722	0.0072499	443.5374	0.9142238	0.9427207
unnatural	0.7594907	0.0072499	443.5374	0.7452423	0.7737392

knitr::kable(pairs(mymeans))

contrast	estimate	SE	df	t.ratio	p.value
natural - unnatural	0.1689815	0.0087075	239	19.40653	0

## quartz_off_screen 
##                 3

## quartz_off_screen 
##                 2

Check order effects

d <- ddply(data_draw, .(ID, Structure, Condition, Section),
                       summarise, correct=mean(correct))
summarySEwithin(data = d,
                measurevar = "correct",
                betweenvars = "Condition",
                withinvars = c("Structure", "Section"),
                idvar = "ID",
                na.rm = T)

## Automatically converting the following non-factors to factors: Section

##   Condition Structure Section   N   correct         sd          se         ci
## 1    social   natural       1  92 0.9018015 0.07646270 0.007971788 0.01583498
## 2    social   natural       2 148 0.9450513 0.07266279 0.005972844 0.01180373
## 3    social unnatural       1 148 0.7429117 0.07266279 0.005972844 0.01180373
## 4    social unnatural       2  92 0.7861614 0.07646270 0.007971788 0.01583498

accuracy_draw_sect <- summarySEwithin(data = data_draw,
                                           measurevar = "correct",
                                           betweenvars = "Condition",
                                           withinvars = c("Structure", "Section", "ID"),
                                           na.rm = T)

## Automatically converting the following non-factors to factors: Section, ID

summ_accuracy_draw_sect <- summarySEwithin(data = data_draw,
                                      measurevar = "correct",
                                      betweenvars = "Condition",
                                      withinvars = c("Structure", "Section"),
                                      idvar = "ID",
                                      na.rm = T)

## Automatically converting the following non-factors to factors: Section

mylm <- lmerTest::lmer(correct ~ Structure*Section + (1|ID),
                       data=accuracy_draw_sect)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	2.8645784	2.8645784	1	238	347.43978	0.0000000
Section	0.2122442	0.2122442	1	238	25.74274	0.0000008
Structure:Section	0.0256530	0.0256530	1	238	3.11141	0.0790286

# Did participants perform better in section 1 or section 2?
# - No difference for unnatural
# - Better in Section 2 for natural
mymeans <- emmeans::emmeans(mylm, ~Section|Structure)
knitr::kable(confint(mymeans))

Section	Structure	emmean	SE	df	lower.CL	upper.CL
1	natural	0.8888889	0.0114765	431.8903	0.8663322	0.9114456
2	natural	0.9530781	0.0090484	431.8903	0.9352937	0.9708624
1	unnatural	0.7509384	0.0090484	431.8903	0.7331541	0.7687228
2	unnatural	0.7732488	0.0114765	431.8903	0.7506921	0.7958055

knitr::kable(pairs(mymeans))

contrast	Structure	estimate	SE	df	t.ratio	p.value
1 - 2	natural	-0.0641892	0.0146145	431.8903	-4.392167	0.0000141
1 - 2	unnatural	-0.0223104	0.0146145	431.8903	-1.526594	0.1275941

# Did participants learn the natural network better than the unnatural network in oth sections?
# - Yes
mymeans <- emmeans::emmeans(mylm, ~Structure|Section)
knitr::kable(confint(mymeans))

Structure	Section	emmean	SE	df	lower.CL	upper.CL
natural	1	0.8888889	0.0114765	431.8903	0.8663322	0.9114456
unnatural	1	0.7509384	0.0090484	431.8903	0.7331541	0.7687228
natural	2	0.9530781	0.0090484	431.8903	0.9352937	0.9708624
unnatural	2	0.7732488	0.0114765	431.8903	0.7506921	0.7958055

knitr::kable(pairs(mymeans))

contrast	Section	estimate	SE	df	t.ratio	p.value
natural - unnatural	1	0.1379505	0.0146145	431.8903	9.439307	0
natural - unnatural	2	0.1798293	0.0146145	431.8903	12.304880	0

Ego Network Effects

# combine drawing data and ego network meaures
data_egodraw <- left_join(accuracy_draw, data_ego)

## Joining, by = "ID"

knitr::kable(head(data_egodraw))

ID	Structure	Condition	correct	degree	betweenness	constraint	transitivity	strength_close	strength_freq	log_degree	log_constraint	strength_close_norm	strength_freq_norm
1	natural	social	0.7777778	5	0.7500000	0.3822222	0.4000000	14	23	1.609438	-0.9617531	2.800000	4.600000
1	unnatural	social	0.7777778	5	0.7500000	0.3822222	0.4000000	14	23	1.609438	-0.9617531	2.800000	4.600000
2	natural	social	1.0000000	9	0.7500000	0.2788066	0.6086957	23	37	2.197225	-1.2772370	2.555556	4.111111
2	unnatural	social	0.6944444	9	0.7500000	0.2788066	0.6086957	23	37	2.197225	-1.2772370	2.555556	4.111111
3	natural	social	0.9722222	10	0.7259259	0.2600722	0.5730337	25	39	2.302585	-1.3467959	2.500000	3.900000
3	unnatural	social	0.7222222	10	0.7259259	0.2600722	0.5730337	25	39	2.302585	-1.3467959	2.500000	3.900000

Degree

Natural structure only
Disappears when constraint added as a covariate

data_egodraw$zdegree <- scale(data_egodraw$degree, center=T, scale = T)


mylm <- lmerTest::lmer(correct ~ Structure*degree + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.4780916	0.4780916	1	238	53.106876	0.0000000
degree	0.0700445	0.0700445	1	238	7.780612	0.0057084
Structure:degree	0.0319298	0.0319298	1	238	3.546797	0.0608800

knitr::kable(emmeans::emtrends(mylm, "Structure", var="degree"))

Structure	degree.trend	SE	df	lower.CL	upper.CL
natural	0.0041466	0.0012339	443.4978	0.0017216	0.0065716
unnatural	0.0013402	0.0012339	443.4978	-0.0010848	0.0037652

mylm <- lmerTest::lmer(correct ~ Structure*log_degree + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.0663911	0.0663911	1	238	7.392435	0.0070323
log_degree	0.0978775	0.0978775	1	238	10.898347	0.0011103
Structure:log_degree	0.0370449	0.0370449	1	238	4.124833	0.0433699

knitr::kable(emmeans::emtrends(mylm, "Structure", var="log_degree"))

Structure	log_degree.trend	SE	df	lower.CL	upper.CL
natural	0.048898	0.0126781	444.5514	0.0239816	0.0738144
unnatural	0.017700	0.0126781	444.5514	-0.0072164	0.0426164

mylm <- lmerTest::lmer(correct ~ Structure*zdegree + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	3.4265689	3.4265689	1	238	380.626542	0.0000000
zdegree	0.0700445	0.0700445	1	238	7.780612	0.0057084
Structure:zdegree	0.0319298	0.0319298	1	238	3.546797	0.0608800

knitr::kable(emmeans::emtrends(mylm, "Structure", var="zdegree"))

Structure	zdegree.trend	SE	df	lower.CL	upper.CL
natural	0.0241268	0.0071792	443.4978	0.0100172	0.0382363
unnatural	0.0077977	0.0071792	443.4978	-0.0063118	0.0219073

"With constraint as a covariate:"

## [1] "With constraint as a covariate:"

mylm <- lmerTest::lmer(correct ~ Structure*degree + log_constraint + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.4780916	0.4780916	1	238	53.1068757	0.0000000
degree	0.0067913	0.0067913	1	237	0.7543888	0.3859689
log_constraint	0.0042915	0.0042915	1	237	0.4767075	0.4905931
Structure:degree	0.0319298	0.0319298	1	238	3.5467967	0.0608800

knitr::kable(emmeans::emtrends(mylm, "Structure", var="degree"))

Structure	degree.trend	SE	df	lower.CL	upper.CL
natural	0.0030386	0.0020249	309.4833	-0.0009457	0.0070229
unnatural	0.0002321	0.0020249	309.4833	-0.0037522	0.0042164

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'
## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Strength

Non-normalized

mylm <- lmerTest::lmer(correct ~ Structure*strength_close + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.5343006	0.5343006	1	238	58.976251	0.0000000
strength_close	0.0752631	0.0752631	1	238	8.307567	0.0043090
Structure:strength_close	0.0183290	0.0183290	1	238	2.023165	0.1562252

knitr::kable(emmeans::emtrends(mylm, "Structure", var="strength_close"))

Structure	strength_close.trend	SE	df	lower.CL	upper.CL
natural	0.0015630	0.0004954	444.3721	0.0005894	0.0025366
unnatural	0.0007097	0.0004954	444.3721	-0.0002639	0.0016833

mylm <- lmerTest::lmer(correct ~ Structure*strength_freq + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.4561104	0.4561104	1	238	50.469281	0.0000000
strength_freq	0.0818157	0.0818157	1	238	9.053029	0.0029045
Structure:strength_freq	0.0236135	0.0236135	1	238	2.612865	0.1073248

knitr::kable(emmeans::emtrends(mylm, "Structure", var="strength_freq"))

Structure	strength_freq.trend	SE	df	lower.CL	upper.CL
natural	0.0010358	0.0003071	444.4305	0.0004323	0.0016393
unnatural	0.0004347	0.0003071	444.4305	-0.0001688	0.0010382

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Normalized

No effect

mylm <- lmerTest::lmer(correct ~ Structure*strength_close_norm + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.1584795	0.1584795	1	238	17.5653265	0.0000392
strength_close_norm	0.0007150	0.0007150	1	238	0.0792516	0.7785588
Structure:strength_close_norm	0.0272060	0.0272060	1	238	3.0154239	0.0837699

knitr::kable(emmeans::emtrends(mylm, "Structure", var="strength_close_norm"))

Structure	strength_close_norm.trend	SE	df	lower.CL	upper.CL
natural	-0.0183356	0.0225497	440.3831	-0.0626541	0.0259829
unnatural	0.0285100	0.0225497	440.3831	-0.0158085	0.0728285

mylm <- lmerTest::lmer(correct ~ Structure*strength_freq_norm + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.1465191	0.1465191	1	238	16.3718884	0.0000704
strength_freq_norm	0.0005597	0.0005597	1	238	0.0625432	0.8027363
Structure:strength_freq_norm	0.0445468	0.0445468	1	238	4.9776146	0.0266097

knitr::kable(emmeans::emtrends(mylm, "Structure", var="strength_freq_norm"))

Structure	strength_freq_norm.trend	SE	df	lower.CL	upper.CL
natural	-0.0201998	0.0178706	439.5091	-0.0553223	0.0149226
unnatural	0.0273732	0.0178706	439.5091	-0.0077492	0.0624957

# overall strength
data_egodraw$strength <- data_egodraw$strength_close_norm + data_egodraw$strength_freq_norm

mylm <- lmerTest::lmer(correct ~ Structure*strength + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.1526566	0.1526566	1	238	17.1159004	0.0000488
strength	0.0008858	0.0008858	1	238	0.0993117	0.7529333
Structure:strength	0.0517915	0.0517915	1	238	5.8068794	0.0167236

knitr::kable(emmeans::emtrends(mylm, "Structure", var="strength"))

Structure	strength.trend	SE	df	lower.CL	upper.CL
natural	-0.0140611	0.0118851	439.1599	-0.0374199	0.0092977
unnatural	0.0200763	0.0118851	439.1599	-0.0032824	0.0434351

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Constraint

Natural structure only
No effect when degree included as covariate

mylm <- lmerTest::lmer(correct ~ Structure*log_constraint + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.1693206	0.1693206	1	238	19.016379	0.0000193
log_constraint	0.0667221	0.0667221	1	238	7.493556	0.0066596
Structure:log_constraint	0.0553747	0.0553747	1	238	6.219123	0.0133178

knitr::kable(emmeans::emtrends(mylm, "Structure", var="log_constraint"))

Structure	log_constraint.trend	SE	df	lower.CL	upper.CL
natural	-0.0549141	0.0148944	442.2287	-0.0841866	-0.0256416
unnatural	-0.0102285	0.0148944	442.2287	-0.0395010	0.0190440

"With Degree as a covariate:"

## [1] "With Degree as a covariate:"

mylm <- lmerTest::lmer(correct ~ Structure*log_constraint + degree + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.1693206	0.1693206	1	238	19.0163784	0.0000193
log_constraint	0.0042446	0.0042446	1	237	0.4767075	0.4905931
degree	0.0067170	0.0067170	1	237	0.7543888	0.3859689
Structure:log_constraint	0.0553747	0.0553747	1	238	6.2191233	0.0133178

knitr::kable(emmeans::emtrends(mylm, "Structure", var="log_constraint"))

Structure	log_constraint.trend	SE	df	lower.CL	upper.CL
natural	-0.0380606	0.0244644	308.7271	-0.0861986	0.0100775
unnatural	0.0066250	0.0244644	308.7271	-0.0415130	0.0547631

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Betweenness

No effect

mylm <- lmerTest::lmer(correct ~ Structure*betweenness + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.3243062	0.3243062	1	238	35.9183816	0.0000000
betweenness	0.0034952	0.0034952	1	238	0.3871067	0.5344198
Structure:betweenness	0.0256151	0.0256151	1	238	2.8369920	0.0934274

knitr::kable(emmeans::emtrends(mylm, "Structure", var="betweenness"))

Structure	betweenness.trend	SE	df	lower.CL	upper.CL
natural	0.0426782	0.0283277	440.5994	-0.0129960	0.0983524
unnatural	-0.0144403	0.0283277	440.5994	-0.0701145	0.0412339

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Transitivity

No effect

mylm <- lmerTest::lmer(correct ~ Structure*transitivity + (1|ID),
                       data=data_egodraw)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	0.5967008	0.5967008	1	238	65.7556876	0.0000000
transitivity	0.0003784	0.0003784	1	238	0.0416954	0.8383760
Structure:transitivity	0.0147775	0.0147775	1	238	1.6284626	0.2031597

knitr::kable(emmeans::emtrends(mylm, "Structure", var="transitivity"))

Structure	transitivity.trend	SE	df	lower.CL	upper.CL
natural	-0.0209835	0.0349006	440.9795	-0.0895757	0.0476088
unnatural	0.0323940	0.0349006	440.9795	-0.0361983	0.1009862

## `geom_smooth()` using formula 'y ~ x'

## `geom_smooth()` using formula 'y ~ x'

Degree, strength, and constraint are highly correlated, and thus redundant. As such, it is unclear which is responsible for learning accuracy.

c <- colnames(data_ego)
knitr::kable(cor(select(data_ego, c[c!="ID"])))

	degree	betweenness	constraint	transitivity	strength_close	strength_freq	log_degree	log_constraint	strength_close_norm	strength_freq_norm
degree	1.0000000	0.2059668	-0.7175133	-0.0857242	0.9621594	0.9798564	0.9348114	-0.8523706	-0.1736306	-0.3847299
betweenness	0.2059668	1.0000000	-0.6376353	-0.8153321	0.1734679	0.1739696	0.2742833	-0.6057811	-0.1788252	-0.3053730
constraint	-0.7175133	-0.6376353	1.0000000	0.4728544	-0.6844266	-0.7073094	-0.8533512	0.9439494	0.2304070	0.4401194
transitivity	-0.0857242	-0.8153321	0.4728544	1.0000000	-0.0490590	-0.0469216	-0.0984351	0.4717161	0.1465413	0.2365039
strength_close	0.9621594	0.1734679	-0.6844266	-0.0490590	1.0000000	0.9610538	0.9010063	-0.8056920	0.0647687	-0.2955944
strength_freq	0.9798564	0.1739696	-0.7073094	-0.0469216	0.9610538	1.0000000	0.9277667	-0.8290160	-0.1142585	-0.2235990
log_degree	0.9348114	0.2742833	-0.8533512	-0.0984351	0.9010063	0.9277667	1.0000000	-0.9017761	-0.1977073	-0.4151050
log_constraint	-0.8523706	-0.6057811	0.9439494	0.4717161	-0.8056920	-0.8290160	-0.9017761	1.0000000	0.2336094	0.4626403
strength_close_norm	-0.1736306	-0.1788252	0.2304070	0.1465413	0.0647687	-0.1142585	-0.1977073	0.2336094	1.0000000	0.3956794
strength_freq_norm	-0.3847299	-0.3053730	0.4401194	0.2365039	-0.2955944	-0.2235990	-0.4151050	0.4626403	0.3956794	1.0000000

cor.test(data_ego$degree, data_ego$log_constraint)

## 
##  Pearson's product-moment correlation
## 
## data:  data_ego$degree and data_ego$log_constraint
## t = -25.146, df = 238, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.8836258 -0.8135519
## sample estimates:
##        cor 
## -0.8523706

Homophily

People are more accurate when images are of the same race

data_draw <- separate(data_draw, col=image1, into=c(NA,"x"), sep="-", remove=F)
data_draw <- separate(data_draw, col=x, into=c("race1", "sex1"), sep=1, remove=T)
data_draw <- separate(data_draw, col=image2, into=c(NA,"x"), sep="-", remove=F)
data_draw <- separate(data_draw, col=x, into=c("race2", "sex2"), sep=1, remove=T)
data_draw$race_homo <- data_draw$race1==data_draw$race2
data_draw$sex_homo <- data_draw$sex1==data_draw$sex2


accuracy_draw_homo <- ddply(data_draw, .(ID, Structure, Condition, race_homo),
                       summarise, correct=mean(correct))


mylm <- lmerTest::lmer(correct ~ Structure*race_homo + (1|ID),
                       data=accuracy_draw_homo)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	5.4601667	5.4601667	1	717	427.42280	0.0000000
race_homo	0.5164630	0.5164630	1	717	40.42881	0.0000000
Structure:race_homo	0.1778519	0.1778519	1	717	13.92227	0.0002056

mymeans <- emmeans::emmeans(mylm, ~Structure*race_homo)
knitr::kable(pairs(mymeans))

contrast	estimate	SE	df	t.ratio	p.value
natural,FALSE - unnatural,FALSE	0.1780556	0.0103177	717	17.257268	0.0000000
natural,FALSE - natural,TRUE	-0.0191667	0.0103177	717	-1.857647	0.2474429
natural,FALSE - unnatural,TRUE	0.1044444	0.0103177	717	10.122828	0.0000000
unnatural,FALSE - natural,TRUE	-0.1972222	0.0103177	717	-19.114915	0.0000000
unnatural,FALSE - unnatural,TRUE	-0.0736111	0.0103177	717	-7.134440	0.0000000
natural,TRUE - unnatural,TRUE	0.1236111	0.0103177	717	11.980475	0.0000000

mymeans <- emmeans::emmeans(mylm, ~race_homo)

## NOTE: Results may be misleading due to involvement in interactions

knitr::kable(pairs(mymeans))

contrast	estimate	SE	df	t.ratio	p.value
FALSE - TRUE	-0.0463889	0.0072957	717	-6.358365	0

## Automatically converting the following non-factors to factors: race_homo

accuracy_draw_homo <- ddply(data_draw, .(ID, Structure, Condition, sex_homo),
                       summarise, correct=mean(correct))


mylm <- lmerTest::lmer(correct ~ Structure*sex_homo + (1|ID),
                       data=accuracy_draw_homo)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
Structure	6.8999220	6.8999220	1	717	669.9863254	0.0000000
sex_homo	0.0068400	0.0068400	1	717	0.6641685	0.4153628
Structure:sex_homo	0.0064455	0.0064455	1	717	0.6258593	0.4291398

Racial homophily affects TP rates in unnatural network (potential ceiling effect in natural network)
No effect on false positive rates

data_draw$sub_reported <- as.numeric(as.logical(data_draw$sub_reported))
report_rates <- ddply(data_draw, 
                      .(ID, Structure, Section, true_structure, race_homo), 
                      summarise, 
                      pos_rate=sum(sub_reported)/length(correct)
                      )
report_rates[report_rates$true_structure, "rate"] <- "TruePositive"
report_rates[!report_rates$true_structure, "rate"] <- "FalsePositive"

mylm <- lmerTest::lmer(pos_rate ~ rate*Structure*race_homo + (1|ID),
                       data=report_rates)
knitr::kable(anova(mylm))

	Sum Sq	Mean Sq	NumDF	DenDF	F value	Pr(>F)
rate	225.9909777	225.9909777	1	1659.518	5428.943204	0.0000000
Structure	0.2541064	0.2541064	1	1659.518	6.104356	0.0135847
race_homo	0.4518528	0.4518528	1	1659.464	10.854784	0.0010062
rate:Structure	12.0572879	12.0572879	1	1659.464	289.650196	0.0000000
rate:race_homo	0.8986488	0.8986488	1	1659.518	21.588089	0.0000036
Structure:race_homo	0.1736872	0.1736872	1	1659.518	4.172458	0.0412439
rate:Structure:race_homo	0.3162420	0.3162420	1	1659.464	7.597028	0.0059104

mymeans <- emmeans::emmeans(mylm, ~race_homo|rate)

## NOTE: Results may be misleading due to involvement in interactions

knitr::kable(pairs(mymeans))

contrast	rate	estimate	SE	df	t.ratio	p.value
FALSE - TRUE	FalsePositive	0.0126526	0.0131770	1655.488	0.9602013	0.3370941
FALSE - TRUE	TruePositive	-0.0743342	0.0132994	1661.187	-5.5892836	0.0000000

mymeans <- emmeans::emmeans(mylm, ~race_homo|rate*Structure)
knitr::kable(pairs(mymeans))

contrast	rate	Structure	estimate	SE	df	t.ratio	p.value
FALSE - TRUE	FalsePositive	natural	0.0059727	0.0186452	1655.826	0.3203316	0.7487574
FALSE - TRUE	TruePositive	natural	-0.0294121	0.0186250	1655.149	-1.5791704	0.1144881
FALSE - TRUE	FalsePositive	unnatural	0.0193326	0.0186250	1655.149	1.0379872	0.2994276
FALSE - TRUE	TruePositive	unnatural	-0.1192563	0.0189896	1666.953	-6.2800774	0.0000000

mymeans <- emmeans::emmeans(mylm, ~Structure|rate*race_homo)
knitr::kable(pairs(mymeans))

contrast	rate	race_homo	estimate	SE	df	t.ratio
natural - unnatural	FalsePositive	FALSE	-0.1428654	0.0186250	1655.149	-7.670605
natural - unnatural	TruePositive	FALSE	0.2273633	0.0186250	1655.149	12.207399
natural - unnatural	FalsePositive	TRUE	-0.1295055	0.0186452	1655.826	-6.945766
natural - unnatural	TruePositive	TRUE	0.1375191	0.0189896	1666.953	7.241801

## Automatically converting the following non-factors to factors: race_homo, rate

Network Learning 2

Miriam Weaverdyck

3/21/2020

Setup

Read in data

Analyses

Ego Network Effects

Degree

Strength

Non-normalized

Normalized

Constraint

Betweenness

Transitivity

Homophily